On the reduction of the degree of linear differential operators

Let L be a linear differential operator with coefficients in some differential field k of characteristic zero with algebraically closed field of constants. Let k^a be the algebraic closure of k. For a solution y, Ly=0, we determine the linear differential operator of minimal degree M and coefficients in k^a, such that My=0. This result is then applied to some Picard-Fuchs equations which appear in the study of perturbations of plane polynomial vector fields of Lotka-Volterra type

Bjorling Problem for Timelike Surfaces in the Lorentz-Minkowski Space

We solve the Bjorling problem for timelike surfaces in the Lorentz-Minkowski space through a split-complex representation formula obtained for this kind of surface. Our approach uses the split-complex numbers and natural split-holomorphic extensions. As applications, we show that the minimal timelike surfaces of revolution as well as minimal ruled timelike surfaces can be characterized as solutions of certain adequate Bjorling problems in the Lorentz-Minkowski space

Humanoid robot kinematic calibration using industrial manipulator

© 2017 IEEE. Kinematic calibration is a crucial task for humanoid robot locomotion. The paper proposes a novel technique for joint offset calibration using industrial manipulator. Corresponding procedure uses position and orientation data from the manipulator and requires fixing of robots bases and end-effectors with respect to each other. The full pose information is obtaining as the humanoid limbs are moved through predefined configurations. To find joint offsets the least-squares optimization problem is solved. The proposed method is accurate since the industrial manipulator provides high precision. The proposed approach was validated on the calibration of AR601M humanoid robot using Kuka iiwa 14 industrial manipulator

Modified spline-based path planning for autonomous ground vehicle

© 2017 by SCITEPRESS - Science and Technology Publications, Lda. All Rights Reserved. Potential function based methods play significant role in global and local path planning. While these methods are characterized with good reactive behavior and implementation simplicity, they suffer from a well-known problem of getting stuck in local minima of a navigation function. In this article we propose a modification of our original spline-based path planning algorithm for a mobile robot navigation, which succeeds to solve local minima problem and adds additional criteria of start and target points visibility to help optimizing the path selection. We apply a Voronoi graph based path as an input for iterative multi criteria optimization algorithm. The algorithm was implemented in Matlab environment and simulation results demonstrate that we succeeded to overcome our original algorithm pitfalls

Comparison of kinematic and dynamic leg trajectory optimization techniques for biped robot locomotion

The paper presents comparison analysis of two approaches in defining leg trajectories for biped locomotion. The first one operates only with kinematic limitations of leg joints and finds the maximum possible locomotion speed for given limits. The second approach defines leg trajectories from the dynamic stability point of view and utilizes ZMP criteria. We show that two methods give different trajectories and demonstrate that trajectories based on pure dynamic optimization cannot be realized due to joint limits. Kinematic optimization provides unstable solution which can be balanced by upper body movement

Automatic mapping and filtering tool: From a sensor-based occupancy grid to a 3D Gazebo octomap

© 2017 IEEE. Robot simulations nowadays provide significant support in testing new algorithms for robotic systems for a broad area of tasks, including navigation, mapping, and SLAM. Within a simulation, special attention should be paid for providing algorithms with realistic testing environments that are to be further used for robot navigation. This paper presents an automatic tool that allows creating realistic landscapes in Gazebo simulation, which are based on results of real world sensor-based exploration. The tool provides automatic filtering and importing of an occupancy grid map into Gazebo framework as a heightmap

Arbitrary trajectory foot planner for bipedal walking

© 2017 by SCITEPRESS - Science and Technology Publications, Lda. All Rights Reserved. This paper presents a foot planner algorithm for bipedal walking along an arbitrary curve. It takes a parametrically defined desired path as an input and calculates feet positions and orientations at each step. Number of steps that are required to complete the path depends on a maximum step length and maximum foot rotation angle at each step. Provided with results of the foot planner, our walking engine successfully performs robot locomotion. Verification tests were executed with AR601M humanoid robot

Comparing fiducial marker systems in the presence of occlusion

© 2017 IEEE. A fiducial marker system is a system of unique 2D (planar) marker, which is placed in an environment and automatically will be detected with a camera with a help of a corresponding detection algorithm. Application areas of these markers include industrial systems, augmented reality, robots navigation, human-robot interaction and others. Marker system designed for such different applications must be robust to such factors as view angles, occlusions, changing distances, etc. This paper compares three existing systems of markers: ARTag, AprilTag, and CALTag. As a benchmark, we use their reliability and detection rate in presence of occlusions of various types and intensity. The paper presents experimental comparison of these markers. The marker detection was performed with a simple inexpensive Web camera

3D modelling and simulation of a crawler robot in ROS/Gazebo

1. Modelling and animation of crawler UGV's caterpillars is a complicated task, which has not been completely resolved in ROS/Gazebo simulators. In this paper, we proposed an approximation of track-terrain interaction of a crawler UGV, perform modelling and simulation of Russian crawler robot "Engineer" within ROS/Gazebo and visualize its motion in ROS/RViz software. Finally, we test the proposed model in heterogeneous robot group navigation scenario within uncertain Gazebo environment. Copyright is held by the owner/author(s). Publication rights licensed to ACM